CLINICAL ORTHOPAEDICS AND RELATED RESEARCH
Number 451, pp. 134–139
© 2006 Lippincott Williams & Wilkins
A New Tool for Measuring Cup Orientation in Total Hip
Arthroplasties from Plain Radiographs
Chen-Kun Liaw, MD; Sheng-Mou Hou, MD, PhD, MPH; Rong-Sen Yang, MD, PhD;
Tai-Yin Wu, MD; and Chiou-Shann Fuh, PhD
agement. The term positioning includes location and orientation. Orientation implies two parameters: abduction
and anteversion.
Abduction can be measured easily using an ordinary
protractor on an anteroposterior (AP) radiograph. Abduction is the angle between the long axis of the ellipse
formed by the cup and the horizontal line of the pelvis.
However, true (anatomic) and planar (radiographic) anteversion are more difficult to measure. Numerous methods
for measurement have been reported.2–6,8–12 The method of
Olivecrona et al requires a computed tomography (CT)
scan and special software.9 The other methods require
high-quality AP radiographs with good patient positioning
and radiographic conditioning. The methods of Lewinnek
et al5 and Pradhan10 are trigonometric methods, which
require a numerical table or a calculator. Long and short
axes of the ellipse need to be drawn in the method of
Lewinnek et al5 and another perpendicular axis located 1⁄5
of the distance along the long axis needs to be drawn in the
method of Pradhan.10 The methods of Fabeck et al4 and
that of Widmer12 do not require a calculator. The method
of Fabeck et al4 takes a longer time to determine the center
of the circle. Widmer’s12 method is better, but it is not
very precise in determining abduction.
We introduce a simple new protractor used to measure
anteversion and abduction using an AP radiograph of the
pelvis.
Orientation of the hip cup is important in total hip arthroplasties. Orientation includes abduction (inclination) and anteversion. Anteversion can be considered as true (anatomic)
and planar (radiographic) anteversion. Some measurement
methods either are too complicated or are less precise. We
developed a new protractor to measure cup orientation using
postoperative anteroposterior radiographs centered at the
hip. The new protractor measures true and planar anteversion and abduction easily and precisely. We verified its accuracy using a software simulator and simulated 45 radiographs of total hip arthroplasties with 15 different anteversions ranging from 15°–29° and 45 actual radiographs of
total hip arthroplasties. We then measured the planar anteversion with our method and the method of Lewinnek et al.
Maximal errors were 3° and 2.61°, respectively, and mean
errors were 0.96° and 1.2°, respectively. The standard deviations were 0.74° with our method and 0.57° with the method
of Lewinnek et al. For the real radiographs, the mean of
absolute difference between the two methods was 1.34°, and
the standard deviation was 1.13°. We found no difference
between the two methods and no difference in our findings
compared with those of Pradhan.
Level of Evidence: Diagnostic study, level II.
According to the American Academy of Orthopaedic Surgeons (AAOS), more than 172,221 total hip arthroplasties
(THAs) are performed annually in the United States.1 Excellent outcomes require technically accurate surgery including proper prosthesis positioning and soft tissue man-
MATERIALS AND METHODS
Received: April 22, 2005
Revised: November 1, 2005; March 18, 2006
Accepted: April 10, 2006
From the En Chu Kong Hospital, Taipei Hsien, Republic of China.
Each author certifies that he or she has no commercial associations (eg,
consultancies, stock ownership, equity interest, patent/licensing arrangements, etc) that might pose a conflict of interest in connection with the
submitted article.
Correspondence to: Chiou-Shann Fuh, PhD, 4F, No. 26, Alley 2, Lane 19,
Shin-Shing Street, Shan-Jia, Shu-Lin City, Taipei County, Taiwan. Phone:
886-2-23936577; Fax: 886-2-23936577; E-mail: [email protected].
DOI: 10.1097/01.blo.0000223988.41776.fa
According to Murray’s definition,8 if the acetabulum axis (or
normal vector of the acetabulum plane) (Fig 1A) is defined, then
the true (anatomic) anteversion can be measured by projecting
the acetabulum axis onto the transverse plane (Fig 1B). Planar
(radiographic) anteversion is measured by projecting the acetabulum axis to the plane perpendicular to the coronal plane and
the acetabulum plane (Fig 1C). Flexion (operative anteversion) is
measured by projecting the same vector onto the sagittal plane
(Fig 1D). Abduction (inclination) is measured by projecting that
134
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Number 451
October 2006
A New Cup Orientation Protractor
135
Fig 1A–E. (A) A photograph shows a pelvis bone model with the acetabulum in
place. The acetabulum axis (black arrow)
is perpendicular to the acetabulum plane.
(B) The true (anatomic) anteversion is
measured by projecting the acetabulum
axis onto the axial plane. (C) Planar (radiographic) anteversion is measured by
projecting the acetabulum axis to the perpendicular plane to the coronal and acetabulum planes. (D) Flexion (operative
anteversion) is measured by projecting the
acetabulum axis onto the sagittal plane.
(E) Abduction (inclination) is measured by
projecting the acetabulum axis onto the coronal plane.
vector onto the coronal plane (Fig 1E).8 These angles are not
independent, because when one angle is changed, so are the
others, unless the vector lies in one of the four planes.
An accepted method of measuring the opening angle ␣P (planar version) is based on the respective lengths of the short (sP)
and long (lP) axes of the elliptical outline of the shell in the AP
radiograph (Fig 2A).5 Using these quantities, the planar version
␣P may be calculated using the formula:
The l is Line AB where the s is Line CD (Fig 2A). When
considering the true version, the principle is the same, but the
equation must be modified to Equation 1.1.11 The st becomes the
distance between the center of the ellipse and the intersection of
the horizontal line passing through the center of the ellipse, as
shown by Line EF (Fig 2B). The lt becomes 1⁄2 the length of the
long axis, as shown by Line DE (Fig 2B).11
␣p = sin−1共sP Ⲑ lP兲
␣t = sin−1共st Ⲑ lt兲
(1)
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(1.1)
136
Clinical Orthopaedics
and Related Research
Liaw et al
Fig 2A–B. (A) A diagram shows the measurements we used on the AP radiograph. We drew a
line from A to B, with point C as the midpoint of the
inferior curve of the ellipse. We then drew a line
from A to C. ␤p is the angle formed by Line AB and
Line AC. (B) When measuring true anteversion of
the AP radiograph, we drew a line from point E (the
top-most point of the semicircle) to point F (the
center of the ellipse). We then selected point G by
the intersection of the horizontal line passing
through point F, and drew a line from E to G. The
angle ␤t is formed by Lines EF and EG.
This method requires a table or calculator with an inverse sine
(sin−1) function and is not convenient. We designed a new protractor to replace the cumbersome calculations.
The method for measuring planar version is as follows: (1)
Draw a line across the maximal diameter of the ellipse in the AP
radiograph, such as Line AB (Fig 2A);
( 2) Determine point C midway on the ellipse (Fig 2A), which
is the intersection of ellipse and the line perpendicular and going
through the midpoint of AB. (3) Draw another line from the apex
A to point C (Fig 2A); and (4) Use an ordinary protractor to
measure the angle ␤P (Fig 2A), which is formed by Lines AC
and AB.
To measure true version: (1) Draw a line from point E (the
top-most point of the semicircle) to point F (the center of the
ellipse) (Fig 2B); (2) Determine point G (Fig 2B) by the intersection of the horizontal line passing through point F; (3) Draw
a line from point E to point G (Fig 2B); and (4) Use an ordinary
protractor to measure the angle ␤t (Fig 2A), which is formed by
lines EG and EF.
␤P = tan−1共sP Ⲑ lP兲
␤t = tan−1共st Ⲑ lt兲
calculate the true and planar versions. By equation 4, we make
the first part of our protractor by marking ␣p (the version) with
␤p (the real angle). This special protractor can be used to measure ␣p directly, with no need for calculations (Fig 3). For the
second part, we used an ordinary protractor to measure abduction. We explained how to measure ␣p directly, and a similar
way to measure ␣t.
To use the protractor, we aligned the base line of the protractor with the long axis of the ellipse to read the planar version
angle defined by point C (Fig 4A–B). To measure the true version angle, we aligned the base line of the protractor with Line
EF, and then read the true version angle defined by point G (Fig
4C–D).
When measuring the planar version, part 2 of our protractor
(an ordinary protractor) can be used simultaneously to measure
(2)
(2.1)
This is deduced from simple trigonometry. In Situation 1, we
measured planar version; sP was the length of short axis and lP
was the length of long axis (Fig 2A). In Situation 2, we measured
true version; st was the length of line FG and lt was the length of
Line EF (Fig 2B).
␣p = sin−1 tan ␤p from Equation 1 and Equation 2
␣t = sin−1 tan ␤t from Equation 1.1 and Equation 1
␤p = tan−1 sin ␣p from Equation 3
␤t = tan sin ␣t from Equation 3.1
-1
(3)
(3.1)
(4)
(4.1)
Using traditional procedures, one would measure angles ␤p and
␤t with an ordinary protractor, then use equations 3 and 3.1 to
Fig 3. The upper part of our protractor is the same as an
ordinary protractor used to measure the abduction angle. The
lower part is used to measure the anteversion angle.
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Number 451
October 2006
A New Cup Orientation Protractor
137
Fig 4A–D. (A) We estimated Point C (arrow) to
determine a 20° planar anteversion angle. The
horizontal line of the pelvis (parallel to the line
passing through both teardrop landmarks) (arrow
H) was 41°, which determined the abduction
angle. (B) The protractor was used with a real radiograph. It shows a planar anteversion angle of
16° and an abduction angle of 32°. (C) The baseline of the protractor was aligned with point E (the
top-most point of the semicircle) and point F (the
center of the ellipse). We determined point G by
the intersection of the horizontal line L passing
through point F. The true version angle was 34° as
measured by point G. (D) The anteversion angle
was 32° when using the protractor with a real radiograph.
the abduction angle. We can read this angle by the protractor of
a horizontal line, which is parallel to the line passing through
both teardrop landmarks, as indicated by the arrow labeled H
(Fig 4A–4B).
We determined the accuracy of our method by comparing it
with the trigonometric method.5,6 We used software simulating
45 radiographs of THAs with 15 different anteversions ranging
from 15°–29° (Fig 5A). We also collected 45 actual radiographs
of THAs. These simulated and real radiographs were printed on
paper. One of the authors (C.K.L.) measured the planar version
of the 45 simulated and 45 real radiographs using the method
described by Lewinnek et al5 (Fig 5B) and 1 week later with our
method (Fig 5C). We randomly ordered the simulated radiographs on each measurement.
The two errors were compared with a two-sample Student’s t
test. Significance was set at the p < 0.05 level.
RESULTS
The median errors were within 1° with our method and
1.23° with the method of Lewinnek et al. Maximal errors
were 3° with our method and 2.61° with the method of
Lewinnek et al, and the mean errors were 0.96° and 1.2°,
respectively. The standard deviation was 0.74° with our
method and 0.57° with the method of Lewinnek et al. (Fig
6) There was no statistical difference between the two
methods. For the real radiographs, the mean of absolute
difference between the two methods was 1.34°, and the
standard deviation was 1.13°.
DISCUSSION
Current methods of measuring the version angle require
good quality radiographs, which means a nearly perfect
AP projection without rotation on the transverse and longitudinal axes, and centered at the hip. If the projection is
not perfect, there will be measurement errors. If there is a
5° rotation on the transverse axis, then it will cause a 5°
error in the flexion angle. A change in one angle causes the
other three angles to change. The changes in the other
three angles (true version, planar version, and abduction)
will be smaller than the flexion angle. Similarly, for the
longitudinal axis, a 5° rotation will cause a 5° error in the
true version. The error of the other three angles will be
smaller. The detailed mathematical formulas were described by Murray.8
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138
Liaw et al
Clinical Orthopaedics
and Related Research
Fig 6. This graph shows the errors of measuring the simulated
version. The method of Lewinnek et al5 and our method
showed good correlation to the real version. There is no systemic variation between the two methods.
Fig 5A–C. (A) The software simulator is shown. The user can
adjust anteversion and wear. (B) The simulated radiographs
were printed on paper to measure the long axis of the ellipse
to determine planar anteversion (the method of Lewinnek et
al5). (C) A photograph shows our protractor used for measuring planar anteversion.
No solution exists for perfect patient positioning using
the plain radiograph method. However, CT can solve this
problem. With a virtual plane as described by McKibben
(including the anterior superior iliac spines and the pubic
tubercles), the software can measure the angle between the
cup and plane.9 The method described by Olivecrona et al9
is excellent but unpractical because of the high cost of CT
and the risk of radiation exposure. The relationship between position and version were discussed by Moritz et
al.7
The greatest error in our method was finding point C
(for planar version) and point F (for true version). In most
patients, the femoral head obscured these points.
Pradhan’s solution was to measure the ellipse by the length
of the perpendicular axis located 1⁄5 of the distance along
the long axis from the apex to avoid the obscured region.10
The point is on middle part of the ellipse. It follows the
rules of an ellipse which makes it easier to estimate. The
mean error and standard deviation of error from Pradhan’s
data were 0.88 and 0.65, respectively.10
Bias in anteversion measurements using radiographs is
inevitable because of measuring a three-dimensional object using a two-dimensional image projection. Some
methods require using a ruler to measure two or more
distances which then are used to make various calculations.5,10 For example, The method of Lewinnek et al
needs measurement of the long and short axes of the ellipse.5 However, with every measurement, operational errors are inevitable. Therefore, we think our method is superior to that of Lewinnek et al. However, this could be the
effect of operational error. Both methods have similar errors; possibly because the femoral head obscured measurement points in our method caused a similar error to the
operational error in the method by Lewinnek et al. The
method of Fabeck et al does not require ruler measurements, as it is determined by lines drawn on a radiograph.4
Our method requires only one measurement, which re-
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
Number 451
October 2006
duces the operational error. Widmer’s method calculates
the measurement using only one step, but there are errors
with different abduction angles.12 Our method can measure without influencing abduction.
Our method is a simplified version of the method of
Lewinnek et al.5 However, we only compared its ability to
measure planar version. Measuring simulated and real radiographs shows little difference between the two methods. We can extend the result to the true version. When
measuring a true version, we need to draw a horizontal line
on the radiograph. However, it is still convenient when
compared with other measurement methods. Our new protractor allows measurement of true version, planar version,
and abduction. Additional studies are needed to provide a
gold standard for measurement.
References
1. AAOS. Total Hip Replacement. Available at: http://orthoinfo.
aaos.org. Accessed October 23, 2005.
2. Ackland MK, Bourne WB, Uhthoff HK. Anteversion of the acetabular cup: measurement of angle after total hip replacement. J Bone
Joint Surg Br. 1986;68:409–413.
3. Coventry MB, Beckenbaugh RD, Nolan DR, Ilstrup DM. 2,012 total
A New Cup Orientation Protractor
4.
5.
6.
7.
8.
9.
10.
11.
12.
139
hip arthroplasties: a study of postoperative course and early complications. J Bone Joint Surg Am. 1974;56:273–284.
Fabeck L, Farrokh D, Tolley M, Descamps PY, Gebhart M, Delince
P. A method to measure acetabulum cup anteversion after total hip
replacement. Acta Orthop Belg. 1999;65:485–491.
Lewinnek GE, Lewis JL, Tarr R, Compere CL, Zimmerman JR.
Dislocations after total hip-replacement arthroplasties. J Bone Joint
Surg Am. 1978;60:217–220.
McLaren RH. Prosthetic hip angulations. Radiology. 1973;107:705–
706.
Moritz T, Ulrich L, Klaus-Arno S, Matthias W, Kai B, Frank L.
Anatomic referencing of cup orientation in total hip arthroplasty.
Clin Orthop Relat Res. 2005;436:144–150.
Murray DW. The definition and measurement of acetabular orientation. J Bone Joint Surg Br. 1993;75:228–232.
Olivecrona H, Weidenhielm L, Olivecrona L, Beckman MO, Stark
A, Noz ME, Maguire GQ, Zeleznik MP, Svensson L, Jonson T. A
new CT method for measuring cup orientation after total hip arthroplasty: a study of 10 patients. Acta Orthop Scand. 2004;75:252–
260.
Pradhan R. Planar anteversion of the acetabular cup as determined
from plain anteroposterior radiographs. J Bone Joint Surg Br. 1999;
81:431–435.
Visser JD, Konings JG. A new method for measuring angles after
total hip arthroplasty: a study of the acetabular cup and femoral
component. J Bone Joint Surg Br. 1981;63B:556–559.
Widmer KH. A simplified method to determine acetabular cup anteversion from plain radiographs. J Arthroplasty. 2004;19:387–390.
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